Taiwanese Journal of Mathematics

PACKING CONSTANTS IN ORLICZ-LORENTZ SEQUENCE SPACES

Yaqiang Yan

Full-text: Open access

Abstract

We discussed the upper and lower bounds of packing constants in Orlicz-Lorentz sequence spaces equipped with both the Luxemburg norm and the Orlicz norm. Provided $\Phi \in \Delta_2(0)$, we showed that the Kottman constant of $\lambda_{\Phi,\omega}$ and $\lambda^o_{\Phi,\omega}$ satisfies $$\max \left\{ \frac{1}{\alpha_\Phi(0)}, \frac{1}{\alpha'_{\Phi,\omega}} \right\} \leq K\left(\lambda_{\Phi,\omega}\right) \leq \frac{1}{\tilde{\alpha}_{\Phi,\omega}},$$ $$ \max \left\{ \frac{1}{\alpha_\Phi(0)}, \frac{1}{\alpha''_{\Phi,\omega}} \right\} \leq K\left(\lambda^o_{\Phi,\omega}\right) \leq \frac{1}{\alpha^{\ast}_{\Phi}}. $$ As a corollary, the packing constant of Lorentz space $\lambda_{p,\omega}$ is $1/(1+2^{1-\frac{1}{p}})$.

Article information

Source
Taiwanese J. Math., Volume 15, Number 6 (2011), 2403-2428.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406478

Digital Object Identifier
doi:10.11650/twjm/1500406478

Mathematical Reviews number (MathSciNet)
MR2896125

Zentralblatt MATH identifier
1262.46013

Subjects
Primary: 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Secondary: 46B20: Geometry and structure of normed linear spaces

Keywords
Orlicz space Orlicz-Lorentz space packing sphere constant Kottman constant

Citation

Yan, Yaqiang. PACKING CONSTANTS IN ORLICZ-LORENTZ SEQUENCE SPACES. Taiwanese J. Math. 15 (2011), no. 6, 2403--2428. doi:10.11650/twjm/1500406478. https://projecteuclid.org/euclid.twjm/1500406478


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